1. Field of the Invention
The present invention relates to a method and device for the braking of wheels in contact with a track, especially but not exclusively wheels of vehicles, through the servo-control of the braking torque applied to each of the wheels of the vehicle. It relates more particularly to the methods and devices in which it is sought to position the value of the braking torque to the maximum possible, taking account of the adherence of the wheel to the track.
2. Description of the Prior Art
The patent application No. FR 91.13119 dated 23rd Oct. 1991 describes a method and device designed for such a use. It is known, according to this application, that the maximum torque that can be exerted by a track on a wheel undergoing a braking force has a value that depends on the slippage of the wheel on the track. For a wheel such as the one shown schematically in FIG. 1a, the value of this torque as a function of the slippage has the aspect of the curve 8 shown in FIG. 1b.
FIG. 1a gives a schematic view of the profile of a wheel 9 that is rotationally attached by a shaft 10, located at the center 0 of the wheel, to a vehicle (not shown). The wheel rotates with a speed .omega., expressed in radians per second, in the direction indicated by the arrow 11. The forces of adherence of the wheel to a track 12, depicted schematically by a line, create a force at the point A of contact between the wheel 9 and the track 12. When a braking torque is applied to the wheel, as the torque tends to reduce the speed, the forces of adherence F create a counter torque for the wheel. The curve 8 of FIG. 1b shows the appearance of the maximum value of the torque, created on the wheel by the forces of adherence between the wheel 9 and the track 12, that can be countered. This maximum value is a function of the value of the slippage of the wheel.
This torque has the value F.times.R, R designating the radius of the wheel.
The curve 8 of FIG. 1b shows that this torque touches a maximum value M for a slippage value g.sub.0. This slippage value characterizes the maximum of the value of the braking torque that can be applied efficiently to the wheel. The corresponding point of the curve 8 having coordinates g.sub.0 M is referenced C.
The patent application No. 91.13119, already mentioned, describes a method and a device aimed at carrying out the braking in such a way that the slippage remains around the value g enabling the efficient application of a maximum braking torque.
The present invention is aimed at obtaining an efficient, low-cost control and regulation device enabling the application, to each of the wheels, as a function of a braking control value, of the optimum braking torque M defined by the curve 8 whenever this is necessary. The phrase "whenever this is necessary" refers to whenever the control value, which shall hereinafter be called "pedal pressure" leads to a torque greater than the optimum torque that can be obtained in view of the slippage of the wheel at this time, this being the case whatever the value of adherence.
For a clear understanding of the invention, we shall return here below to the meaning given to slippage and to the way in which the coefficient of slippage g is applied, as well as to the way in which the operating point shifts when it is not on the curve 8.
Slippage is generally defined by a coefficient of slippage g, expressing the percentage represented by the speed of slippage in the total speed of the vehicle. ##EQU1##
In the formula (1) above, V.sub.V is the speed of the vehicle, V.sub.r is the speed resulting from the rotation speed .omega. of the wheel (Vr=.omega.R).
If we consider a straight line .DELTA. with a y-axis value C.sub.1 below the maximum M defined on the curve 8 by the point C having the x-axis value g.sub.0, this straight line crosses three zones. The first zone 15 is above the curve 8 and to the left of a straight line 13 having an x-axis value g.sub.0 shown in dashes. A second zone 16 is between the curve 8 and the x-axis and finally a third zone 17 is above the curve 8 to the right of the straight line 13 having an x-axis value g.sub.0.
When the slippage has a value g.sub.1, for example at the point having coordinates g.sub.1 C.sub.1, it means that the braking torque is greater than the maximum torque C'.sub.1 that the forces of adherence can put up against this slippage value. The rotation speed .DELTA. of the wheel corresponding to a running speed V.sub.R will decrease faster than the speed V.sub.V of the vehicle, and the slippage will therefore be increased until it reaches the value of slippage g'.sub.1 corresponding to the x-axis value of the point B where the straight line .DELTA. intersects the curve 8 for the first time. This point is a point of equilibrium where the torque produced by the forces of adherence is equal to the torque exerted by the braking forces. The point of operation will therefore get stabilized at the point B.
If the torque C.sub.1 is exerted while the slippage has the value g".sub.1 corresponding to a point of the straight line located in the zone 16, it means that the torque C.sub.1 is lower than the torque C".sub.1 that may be put up as an opposing torque by the forces of adherence for this value of slippage. The speed .DELTA. of the wheel corresponding to the running speed V.sub.R will therefore get reduced less quickly than the speed V.sub.V of the vehicle. The slippage will get reduced until it returns to the point B.
It is noted that if the slippage coefficient diminishes, it means that the point of operation is within the zone 16 where it is definitely possible to increase the efficiency of the braking by increasing the braking torque.
If the braking torque C.sub.1 is exerted while the value of the slippage has the value g"'.sub.1 so that the point having coordinates C.sub.1, g"'.sub.1 is in a zone where the braking torque is greater than the torque that can be exerted by the adherence forces, the rotational speed .omega. of the wheel corresponding to the running speed V.sub.R of the vehicle will get diminished more quickly than the speed of the vehicle, and the slippage will increase. In this case, if it is desired to reach a point of equilibrium from which it is possible again to increase the braking torque to a value close to its maximum value is reached, it is necessary to reduce the braking torque to a value where operation is within the zone 16, the zone within which it is possible, by gradually increasing the braking torque, to reach the point of operation defined by the point C where the braking efficiency is the maximum.
It is observed that the zone 17 includes the entire zone located above a line 14 constituted, firstly, by the straight line segment joining the point of the y-axis having the y-axis value M and the point C having the coordinates (g.sub.0.M) and, secondly, the part of the curve 8 located to the right of the point C.
The curve 8 still has substantially the aspect shown in FIG. 1b, but the values of M, g.sub.0 and even the precise shape of the curve depend on the nature of the track, especially its paving, the nature of the wheel tire and many other parameters such as, for example, the inflation pressure of the tires, the load of the wheel under the weather conditions etc.
This is why, according to the invention, in order
in to obtain the maximum braking efficiency and work the neighborhood of the point C of the curve, there is provision for servo-linking the braking torque to variables that depend directly or indirectly on the slippage value of the wheel.
Such variables are first of all the slippage itself, and values representing, with respect to the slippage, derivatives with respect to other magnitudes such as time or the derivative of the braking torque with respect to the slippage. The derivatives may be first order, second order or higher order derivatives.
It has been seen further above that the zones 15, 16, 17 still exist but that they are variable as a function of the position of the curve 8 in the plane and of its real form which is known only approximately. For this reason, it has been chosen to process the variables depending on the slippage by fuzzy logic. In this way, it is possible to take account of the range of values to which the real value of a variable belongs rather than the value of the variable itself.
If the input variables, their different ranges and the rules fixing the output magnitudes as a function of the ranges to which the real value of the input variables belong are well chosen, the fuzzy logic systems make it possible to obtain very high efficiency at lower cost than with a computer working in P.I.D. (Proportional Integral Derivative) mode.
The standard mode of regulation with a P.I.D. necessitates the application of linear digital equations. These equations must simulate the behavior of the system that they regulate as efficiently as possible. The limits of the P.I.D. are reached when these mathematical equations have to simulate human or subjective ideas or when the physical system becomes too complex to be modelized with precision (because of non-linearities, degradation of the physical characteristics, etc.), or when this simulation can be achieved but requires an equation for each situation. It is at this level that fuzzy logic becomes useful.
Indeed, it enables the definition of rules of inference that increasingly approach human forms of experience and reasoning.
The explanations given here above on the value of the maximum effective torque that can be applied will be capable of being used, by means of a fuzzy logic computer, to define input and output magnitudes of such a computer as well as for the qualitative definition of the actions to be taken on the output values for each of the combinations of the input magnitudes. It will then be necessary to define a rule of "defuzzification" making it possible to pass from the recommended qualitative actions to quantified actions.
It is these quantified actions that will determine the real value of the output magnitudes within the recommended ranges.
According to the invention, the input magnitudes are:
the value of the coefficient of slippage g of the wheel on the track, this value being defined by the foregoing formula (1); PA1 the value of the derivative of the braking torque with respect to the slippage, namely ##EQU2## .DELTA.g and .DELTA.c designating the algebraic increases of the slippage and of the braking torque during one and same small period of time. It will be seen that, in one embodiment, this period is 5 ms. This value is given in order to provide a better definition of the qualifier "small". This value can obviously be smaller or greater. It is not obligatory that this value should remain constant. In particular, it is not ruled out that the measurement of .DELTA.g and .DELTA.c should be done periodically at times when these values have greater significance than at other times, for example at times when the weight exerted by the vehicle On the wheel is sufficient. PA1 the value of the derivative of the slippage in relation to time, namely ##EQU3## .DELTA.g designates the algebraic increase of the slippage in the course of time .DELTA.t, .DELTA.t representing the time that has elapsed since the preceding measurement of g. PA1 in making an iterative computation, according to the principles of fuzzy logic, of an output magnitude representing an algebraic increase of a preceding value of the braking torque, the computation being done on the basis of input magnitudes that depend directly or indirectly on the value of the coefficient of slippage of the wheel on the track, PA1 in comparing the corrected value of the braking torque with a control value of this torque PA1 and, if necessary, in limiting the last increase computed so that the computed value of the torque is at most equal to a control value, PA1 finally in applying the computed torque to a braking device. PA1 the fixing, for each input magnitude, of a number of continuous qualitative ranges and of a number of continuous qualitative zones for the output magnitude, each of the ranges or zones comprising all the values extending from a minimum value to a maximum value, these two values constituting the limits of the range or zone; PA1 the assigning of a coefficient of membership ranging from 1 to 0 to each value of each range or zone; PA1 the assigning, to each combination of three ranges that can be constituted with a range of each of the input values, of a number identifying one of the qualitative zones of the output value; PA1 the assigning, to each zone, of the output value of a weight which is a magnitude proportional to a surface demarcated by a segment whose length is equal to the length of the zone, by a curve representing, in a direction perpendicular to the segment, the value of the coefficient of membership in the zone of each value of the segment and, possibly, by perpendiculars to the segment that are taken to its ends; PA1 the defining of a rule to determine a quantified output value from qualitative zones designated by each of the combinations that can be constituted with a range to which belongs each of the three input values, measured during the subsequent performance of the method, the rule stipulating that the quantified value is a function of the weight of each of the designated zones and, for each of them, a function of a coefficient of weight which is itself a function of the coefficients of membership of each real measured value in the range participating in the combination that designates the output qualitative zone.
Hereinafter in the explanation, the variable ##EQU4## shall be called the slope, or the slippage slope, the torque being expressed in newton-meters. The slope will be expressed by a number obtained by division of .DELTA.g by .DELTA.c and multiplication by 10,000. The derivative of the slippage in relation to time shall be called dslip. It will be expressed by a number representing the increase of g during periods equal to 5 milliseconds.
The output value of the computer is the correction value to be applied to the braking torque exerted by the braking means of the vehicle on the wheel.
The input and output magnitudes being chosen, it will be necessary, in accordance with the known principles of fuzzy logic, to define, for each input magnitude, firstly different qualitative ranges, the passing from one range to another corresponding to a change in qualitative action on an output magnitude and, secondly, for each of the ranges, the degree of membership, in this range, of each particular value of the range. According to one embodiment of the present invention, the slope has been divided into four ranges, two ranges with a low slope, one range with a
steep negative slope and one range with a positive steep slope. The two ranges with a low declivity are those that are in the neighborhood of the point C of the curve 8. It will be sought to work in these two ranges of slopes and, for this purpose, to exert an action on the braking torque tending to bring the value of the slippage coefficient around the value g.sub.0.
The slippage input magnitude has been divided into three ranges, one range for the low slippages called low-slip, one range for the medium slippages called medium-slip and one range for the high slippages called high-slip. The input magnitude dslip has been divided into two ranges low Dslip and high Dslip.
The output variable is a value of pressure variation control in a device that applies friction elements to a part linked to the wheel, for example a brake shoe on a disk. This magnitude is directly related to the variation of the braking torque by a known mathematical relationship. Hereinafter, it will be likened to the variation of the braking torque.
The pressure variable has been divided into seven zones numbered 7 to 1. The pressure variation is a pressure that is algebraically added to the already existing pressure. The modifications of the pressure are applied with the same frequency as the frequency of measurement of the input variables.
The pressure zones 7 to 4 have negative values for the system works by the withdrawal or lowering of pressure to an initial pressure that is generally too high, i.e. a pressure that corresponds to a braking torque located above the maximum M of the curve 8. The zones numbered 3 and 2 are zones that include the value 0 and are, on the whole, close to 0 with values that are negative by a majority for the zone 3 and positive by a majority for the zone 2.
The logic of the computer is designed so that the correction of the braking torque remains within the spans of values included between these two zones.
This means that the zones 1 and 4 to 7 are used, in principle, in a transient phase at the start of the braking so as to take the point of operation of the brakes or, as the case may be, speedily bring this point of operation, in the plane defined by the slippage and breaking torque, to the neighborhood of the point C.
The zones 2 and 3 are then used to keep the point of operation in this neighborhood.
The zone 1 corresponds to low positive values for the braking is, as explained further above, essentially controlled by withdrawal to a pressure that initially is excessively high. This initial pressure is controlled by the pedal pressure value. In the method according to the invention, the output value of the modified pressure torque is compared with the controlled value, in such a way that the controlled value is applied when this value is smaller than the computed value. The above explanations are given to provide an understanding of how the computed variations of positive pressure, represented by the zone 1 of the output value, may keep a low value without harming the efficient operation of the braking.
The input magnitudes chosen above, the number of qualitative ranges for each of the input magnitudes and the number of qualitative zones for the output value are given by way of an example to make it easier to understand the invention. Other choices are possible without departing from the field of the invention.
For each of the ranges of the different input magnitudes and each of the zones of the different output magnitudes, there is defined a coefficient of membership, in this range or zone, of each value of the range or zone.
In a plane referenced by two axes of coordinates, where the x-axis carries the values of the magnitude and the y-axis carries the values of the membership coefficients, the ranges or zones and their membership coefficients are represented, firstly, by a segment on the x-axis and, secondly, by an arc of a curve whose y-axis value ranges from 0 to 1. The ends of the segment define the x-axis values of the limits of each range. The x-axis values of the ends of the segment are also the x-axis values of the ends of the arc of a curve representing the coefficient of membership, in a range, of a value of the range.
A definition shall now be given of the rules by which it is possible to pass from one set of qualitative input ranges, these ranges being defined by the membership of a real input value in the range, to a zone of output values.
In the exemplary embodiment of the present invention, there are three input variables and only one output magnitude.
It is therefore possible to define a 3D space by a system of axes of coordinates where each axis corresponds to an input magnitude and carries the different qualitative ranges of the input magnitudes defined here above. Although the qualitative ranges of a magnitude as defined further above may have mutually overlapping zones, it is specified to all ends and purposes that the qualitative ranges defined on each axis of the 3D space are ranges that correspond solely to a qualitative value of each input variable. They therefore do not overlap. It is also specified that this representation is not obligatory. It is aimed solely at making it easier to understand the rules that will be applied.
Two ranges have been defined on the magnitude dslip. The axis dgliss will carry two segments, each representing one of the ranges. Similarly, the slippage axis will have three segments and the slope axis will have four segments. These different segments enable the defining of 4.times.3.times.2=24 cubes of the 3D space created. Each cube thus corresponds to a single combination of qualitative ranges of the three input variables and the set of 24 cubes represents all the possible combinations. A particular combination of real values of input variables, the input values measured at an instant, designates one or more cubes if a variable belongs simultaneously to several ranges. The qualitiative values of the output magnitude contained in these cubes constitute the designated qualitative values of the output magnitude.
For each of these cubes, where each value belongs to only one zone, an output qualitative zone of the output magnitude must be defined. It is again observed at this stage that, owing to the possible overlapping of the ranges of the input values, a same input magnitude value may be present on several qualitative ranges.
It follows therefrom that a set of three real inputs may lead to several of the 24 cubes of the 3D space. Each of the cubes that is reached contains only one qualitative value of the output variable, but each of the cubes thus designated may contain a zone of output values that is identical to or different from the other designated zones which are in the other cubes corresponding to the three values of the input magnitudes. Even if only one of the 24 cubes is designated by the 3 input values, the value of the output magnitude contained in this cube is a qualitative value that must be converted into a quantified value. The object of the "defuzzification" rules is to determine a quantified value for the output magnitude when the exploitation of the qualitative rules leads to one or more qualitative values of the values of the output magnitude. Before speaking of the defuzzification rules, the distribution of the magnitudes in the 24 cubes of the 3D space shall be defined here below. This distribution is defined by the presence of a numeral, extending from 1 to 7, in each of the 24 cubes. A sharing of the cubes between a high dslip and a low dslip leads to two 2D spaces (slope and slippage) enabling the constitution of two matrices.
The matrix corresponding to a high dslip is uniformly filled with sevens, i.e. pressure is removed to the greatest possible extent. This matrix makes it possible to limit the speed of the rising of the slippage in the positive slope zone and in the negative slope zone. In the positive slope zone, this rule makes it possible not to pass the peak C too swiftly and, in the negative slope zone, it makes it possible not to go too far in the high values of slippage.
The second matrix corresponds to lower variations of slippage. For this matrix, the following rules apply:
If the slippage is too high (3rd line of the matrix) then, regardless of the value of the slope, it is necessary to remove a great deal of pressure (but less than when there is a start towards locking triggered by high dslip) by means of the zone 6 (pressure ----).
If the slippage is medium (2nd line of the matrix), then it is still necessary to remove pressure, whatever may be the slope. A little less pressure must be removed for the maximum M hence zone 5 is being approached (pressure ---).
If the slippage is small (first line of the matrix), namely in the normal zone, then the value of the slope may come into play.
If the slope is highly negative (slope --), then pressure must be removed but moderately, hence zone 4 (pressure --).
If the slope is negative (slope -) then it is necessary to remove a little pressure, hence zone 3 (pressure -).
If the slope is positive (slope +), then it is necessary to add a little pressure, hence zone 2 (pressure +) .
If the slope is highly positive (slope ++), then it is necessary to add much pressure, hence zone 1 (pressure ++).
The regulator must actually get stabilized between the zones 2 and 3 to keep low pressure variations and remain in the region of the maximum.
The rules of "defuzzification" will now be explained. These rules bring into play the coefficients of membership of the input variables. They also bring into play a coefficient of weight for each of the qualitative output values designated by the real values of the input magnitudes.
The rule chosen is that each designated zone of output values comes into play with a weight coefficient that is equal to the value of the smallest of the coefficients of membership of the three input magnitudes leading to this zone. This rule can be applied directly to the qualitative values of pressure 1, 2, 3 and 4 which, since they are in only one of the 24 cubes, can be designated only once. It may happen, on the contrary, that the qualitative values 5, 6, 7 which are in several cubes are designated several times. In this case, each cube will be examined to find out which coefficient of membership of each of the three magnitudes is the smallest and, of the coefficients thus selected, the greatest will be kept. It is this greatest of the smallest coefficients that will be equal to the coefficients of weight of the qualitative value. The notion of coefficient of weight shall now be specified by the use made thereof to arrive at a quantified output value from the designated qualitative values and their coefficients of weight. It is now necessary to work on the plane defined by the zone of value of the variations of output pressure and coefficients of membership in these zones. If a uniform weight per unit of area is assigned to this plane, the weight of each zone is defined as the weight of the part of the plane demarcated by the x-axis, by the curve defining the coefficient of membership, in the zone, of each value of the zone, by a straight line parallel to the x-axis and at a distance, from this straight line, that is equal to the coefficient of weight chosen for the zone as a function of the coefficients of membership of the input variables as explained further above and, as the case may be, by perpendiculars to the x-axis taken through the limit points of the zone.
The quantified output value is equal to the x-axis value of the center of gravity of all the surfaces defined here above.